Description
Book SynopsisPresents a study of problems related to the theory of infinite-dimensional dynamical systems. This work studies their properties for various non-autonomous equations of mathematical physics: the 2D and 3D Navier-Stokes systems, reaction-diffusion systems, dissipative wave equations, the complex Ginzburg-Landau equation, and others.
Table of ContentsIntroduction Attractors of autonomous equations: Attractors of autonomous ordinary differential equations Attractors of autonomous partial differential equations Dimension of attractors Attractors of non-autonomous equations: Processes and attractors Translation compact functions Attractors of non-autonomous partial differential equations Semiprocesses and attractors Kernels of processes Kolmogorov $\varepsilon$-entropy of attractors Trajectory attractors: Trajectory attractors of autonomous ordinary differential equations Attractors in Hausdorff spaces Trajectory attractors of autonomous equations Trajectory attractors of autonomous partial differential equations Trajectory attractors of non-autonomous equations Trajectory attractors of non-autonomous partial differential equations Approximation of trajectory attractors Perturbation of trajectory attractors Averaging of attractors of evolution equations with rapidly oscillating terms Proofs of Theorems II.1.4 and II.1.5 Lattices and coverings Bibliography Index.
